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The aim of this study is to investigate the stability properties of a model of the lac operon enhanced with stochastic perturbations. New sufficient conditions of exponential mean square stability are obtained analytically for this model and threshold values derived. For regulatory networks, an observer method for the dynamic of the lac operon model is employed, that uses the measured input and output...
We present a novel phase-amplitude model for noisy oscillators described by Itô stochastic differential equations. The model is completely rigorous and it holds for any value of the noise intensity. The phase and amplitude equations depend on the choice of an appropriate set of basis vectors. We show that using Floquet's basis, a phase-amplitude description is obtained analogous to others, previously...
When sound propagates in the shallow ocean, source characteristics complicate the analysis of received acoustic data considerably especially when they are broadband and spatially complex. Noise whether ambient, distant shipping, wind blown surface generated complicates this already chaotic environment even further primarily because these disturbances propagate through the same inherent oceanic medium...
The dynamics of a nonlinear cutting process in the presence of random noise is defined and investigated. This approach is adequate for a wide range of models describing the orthogonal metal cutting processes as an oscillator where nonlinearity comes from the cutting force. The method of Lyapunov-Krasovskii functional was adopted to analyse the system. The conditions ensuring an asymptotic stability...
We review briefly basic Melnikov theory for both deterministic and stochastic systems. We then show how the theory can be used for the identification of a class of multistable systems for which experimental data are available on the relation between excitation frequency and rate of escape from a potential well. We illustrate our approach for the case of the auditory nerve fiber, for which the use...
This paper is on the constant gain extended Kalman filter (CGEKF) with exponential data weighting as a state estimator for nonlinear stochastic systems. In particular we state that under certain conditions the estimation error is exponentially bounded in mean square and further uniformly stochastically bounded. These theoretical results are verified by numerical simulations, where we present some...
This work presents new results for state estimation based on noisy observations suffering from two different types of uncertainties. The first uncertainty is a stochastic process with given statistics. The second uncertainty is only known to be bounded, the exact underlying statistics are unknown. State estimation tasks of this kind typically arise in target localization, navigation, and sensor data...
This paper deals with some aspects concerning to the practical implementation of the stochastic gradient algorithms in active control. The control system under study is assumed to be a multichannel feedforward system and it is also assumed that there is not feedback signals from the secondary sources measured at the detection sensors. Several iterative algorithms were developed in [1] [2] for a frequency...
A new recursive algorithm is proposed for finding the minimum of an objective function whose gradient is not obtainable directly but is approximated from the noisy observations of the function. The algorithm is based on the simultaneous perturbation stochastic approximation method (SPSA) combined with randomly varying truncations, and provides the estimate, which is convergent under weaker conditions...
We present a method to identify the parameters of a state space model for a max-plus-linear discrete event system from measured data. Previous papers report on results with noise-free measured data. In this paper we extend this to identification for perturbed max-plus-linear systems in a stochastic setting. The approach is based on recasting the identification problem as an optimization problem. We...
This paper studies the design of a set of outgoing radar signals to discriminate between two target classes. We model the reflectivity function of each target by a two-dimensional stochastic process to account for uncertainties and propagation effects. The signals are selected to minimize the expected number of transmissions that are needed to guarantee a given confidence level in the classification...
Recent empirical research has discovered that linkages among fMRI signals of the brain in resting-state have meaningful temporal variations. Most current studies of brain networks assume that these linkages are constant. We propose a model and an accompanying algorithm to infer and track changes in these interaction strengths, thus providing a more comprehensive way to study brain dynamics. The stochastic...
Model-based single-channel source separation (SCSS) is an ill-posed problem requiring source-specific prior knowledge. In this paper, we use representation learning and compare general stochastic networks (GSNs), Gauss Bernoulli restricted Boltzmann machines (GBRBMs), conditional Gauss Bernoulli restricted Boltzmann machines (CGBRBMs), and higher order contractive autoencoders (HCAEs) for modeling...
We consider networks of agents cooperating to minimize a global objective, modeled as the aggregate sum of regularized costs that are not required to be differentiable. Since the subgradients of the individual costs cannot generally be assumed to be uniformly bounded, general distributed subgradient techniques are not applicable to these problems. We isolate the requirement of bounded subgradients...
The paper presents a method for estimating the parameter of a Potts model jointly with the unknowns of an image segmentation problem. The method addresses piecewise constant images degraded by additive noise. The proposed solution follows a Bayesian approach, that yields the posterior law for all the unknowns (labels, gray levels, noise level and Potts parameter). It is explored by means of MCMC stochastic...
Dropout and DropConnect can be viewed as regularization methods for deep neural network (DNN) training. In DNN acoustic modeling, the huge number of speech samples makes it expensive to sample the neuron mask (Dropout) or the weight mask (DropConnect) repetitively from a high dimensional distribution. In this paper we investigate the effect of Gaussian stochastic neurons on DNN acoustic modeling....
Tracking problems are usually investigated using the Bayesian approach. Many practical tracking problems involve some unknown deterministic nuisance parameters such as the system parameters or noise statistical parameters. This paper addresses the problem of state estimation in linear discrete-time dynamic systems in the presence of unknown deterministic system parameters. A Cramér-Rao-type bound...
New filters are derived for estimating the n-dimensional state of a linear dynamic system based on uncertain m-dimensional observations, which suffer from two types of uncertainties simultaneously. The first uncertainty is a stochastic process with given distribution. The second uncertainty is only known to be bounded, the exact underlying distribution is unknown. The new estimators combine set theoretic...
Volatility of the stock price is the key to the pricing problem of stock related derivatives in finance. Volatility appears in the diffusion term of the usual modeling of stock prices. One popular approach is to take volatility to be stochastic, and assumes that it satisfies a stochastic differential equation. Taking the stock price to be the observation, we may then pose the filtering problem of...
This paper studies the data driven update of a model for a system where the number of inputs or outputs increased. Often existing control systems are equipped with an additional sensor or actuator to improve performance. If a good model for the present system is available it is advantageous to only estimate the additional part while keeping the present model, compared to estimating the whole model...
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